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y=(arctgx)/(sinx+cosx)
Derivada de la función/ arctg/ sinx+cosx/ y=(arctgx)/(sinx+cosx)

Derivada de y=(arctgx)/(sinx+cosx)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
    acot(x)    
---------------
sin(x) + cos(x)
acot⁡(x)sin⁡(x)+cos⁡(x)\frac{\operatorname{acot}{\left(x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}} 
acot(x)/(sin(x) + cos(x))
Gráfica
02468-8-6-4-2-1010-20002000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
              1                (-cos(x) + sin(x))*acot(x)
- -------------------------- + --------------------------
  /     2\                                          2    
  \1 + x /*(sin(x) + cos(x))       (sin(x) + cos(x))
(sin⁡(x)−cos⁡(x))acot⁡(x)(sin⁡(x)+cos⁡(x))2−1(x2+1)(sin⁡(x)+cos⁡(x))\frac{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{acot}{\left(x \right)}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}} - \frac{1}{\left(x^{2} + 1\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)}
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Segunda derivada [src] 
/                        2\                                                 
|    2*(-cos(x) + sin(x)) |              2*x         2*(-cos(x) + sin(x))   
|1 + ---------------------|*acot(x) + --------- - --------------------------
|                       2 |                   2   /     2\                  
\      (cos(x) + sin(x))  /           /     2\    \1 + x /*(cos(x) + sin(x))
                                      \1 + x /                              
----------------------------------------------------------------------------
                              cos(x) + sin(x)
2x(x2+1)2+(2(sin⁡(x)−cos⁡(x))2(sin⁡(x)+cos⁡(x))2+1)acot⁡(x)−2(sin⁡(x)−cos⁡(x))(x2+1)(sin⁡(x)+cos⁡(x))sin⁡(x)+cos⁡(x)\frac{\frac{2 x}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}} + 1\right) \operatorname{acot}{\left(x \right)} - \frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\left(x^{2} + 1\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}}
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Tercera derivada [src] 
    /                        2\     /         2 \   /                        2\                                                         
    |    2*(-cos(x) + sin(x)) |     |      4*x  |   |    6*(-cos(x) + sin(x)) |                                                         
  3*|1 + ---------------------|   2*|-1 + ------|   |5 + ---------------------|*(-cos(x) + sin(x))*acot(x)                              
    |                       2 |     |          2|   |                       2 |                                                         
    \      (cos(x) + sin(x))  /     \     1 + x /   \      (cos(x) + sin(x))  /                                 6*x*(-cos(x) + sin(x))  
- ----------------------------- - --------------- + ------------------------------------------------------ + ---------------------------
                   2                         2                         cos(x) + sin(x)                               2                  
              1 + x                  /     2\                                                                /     2\                   
                                     \1 + x /                                                                \1 + x / *(cos(x) + sin(x))
----------------------------------------------------------------------------------------------------------------------------------------
                                                            cos(x) + sin(x)
6x(sin⁡(x)−cos⁡(x))(x2+1)2(sin⁡(x)+cos⁡(x))+(6(sin⁡(x)−cos⁡(x))2(sin⁡(x)+cos⁡(x))2+5)(sin⁡(x)−cos⁡(x))acot⁡(x)sin⁡(x)+cos⁡(x)−3(2(sin⁡(x)−cos⁡(x))2(sin⁡(x)+cos⁡(x))2+1)x2+1−2(4x2x2+1−1)(x2+1)2sin⁡(x)+cos⁡(x)\frac{\frac{6 x \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)} + \frac{\left(\frac{6 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}} + 5\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{acot}{\left(x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}} - \frac{3 \left(\frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}} + 1\right)}{x^{2} + 1} - \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}}{\sin{\left(x \right)} + \cos{\left(x \right)}}
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Gráfico
Derivada de y=(arctgx)/(sinx+cosx)
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